In structured prediction, target objects have rich internal structure which does not factorize into independent components and violates common i.i.d. assumptions. This challenge becomes apparent through the exponentially large output space in applications such as image segmentation or scene graph generation. We present a novel PAC-Bayesian risk bound for structured prediction wherein the rate of generalization scales not only with the number of structured examples but also with their size. The underlying assumption, conforming to ongoing research on generative models, is that data are generated by the Knothe-Rosenblatt rearrangement of a factorizing reference measure. This allows to explicitly distill the structure between random output variables into a Wasserstein dependency matrix. Our work makes a preliminary step towards leveraging powerful generative models to establish generalization bounds for discriminative downstream tasks in the challenging setting of structured prediction.

翻译：在结构化预测中，目标对象具有丰富的内部结构，该结构既不能分解为独立分量，又违反了常见的独立同分布假设。这一挑战在图像分割或场景图生成等应用中通过指数级增长的输出空间变得尤为显著。我们提出了一种用于结构化预测的新型PAC-贝叶斯风险界，其中泛化速率不仅随结构化样本数量扩展，还随其规模扩展。其基本假设符合当前关于生成模型的研究趋势：数据是通过将参考测度因子化的Knothe-Rosenblatt重排生成的。这使我们能够将随机输出变量之间的结构显式提炼为一个Wasserstein依赖矩阵。我们的工作迈出了初步一步，旨在利用强大的生成模型，在结构化预测这一具有挑战性的场景中，为判别式下游任务建立泛化界限。